Multi-Battle Contests: An Experimental Study

Mago, Shakun and Sheremeta, Roman (2016): Multi-Battle Contests: An Experimental Study. Forthcoming in: Southern Economic Journal

Abstract

We examine behavior of subjects in simultaneous and sequential multi-battle contests, where each individual battle is modeled as an all-pay auction with complete information. In simultaneous best-of-three contests, subjects are predicted to make positive bids in all three battles, but we find that subjects often make positive bids in only two battles. In sequential contests, theory predicts sizable bids in the first battle and no bids in the subsequent battles. Contrary to this prediction, subjects significantly underbid in the first battle and overbid in subsequent battles. Consequently, instead of always ending in the second battle, contests often proceeds to the third battle. Finally, although the aggregate bid in simultaneous contests is similar to that in sequential contests, in both settings, subjects make higher aggregate bids than predicted. The observed behavior of subjects can be rationalized by a combination of multi-dimensional iterative reasoning and a non-monetary utility of winning.

• Item Type: MPRA Paper
• Language: English
• Keywords: multi-battle contest, experiments, iterative reasoning, overdissipation
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior

References

Altmann, S., Falk, A., & Wibral, M. (2012). Promotions and incentives: The case of multi-stage elimination tournaments. Journal of Labor Economics, 30, 149-174.

Amegashie, J.A., Cadsby, C.B., & Song, Y. (2007). Competitive burnout: Theory and experimental evidence. Games and Economic Behavior, 59, 213-239.

Arad, A. (2012). The tennis coach problem: A game-theoretic and experimental study. The B.E. Journal of Theoretical Economics, 12, 10.

Arad, A., & Rubinstein, A. (2012). Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game. Journal of Economic Behavior and Organization, 84, 571-585.

Avrahami, J., & Kareev, Y. (2009). Do the weak stand a chance? Distribution of resources in a competitive environment. Cognitive Science, 33, 940-950.

Avrahami, J., Kareev, Y., Todd, P.M., & Silverman, B. (2014). Allocation of resources in asymmetric competitions: How do the weak maintain a chance of winning? Journal of Economic Psychology, 42, 161-174.

Baye, M., & Hoppe, H. (2003). The strategic equivalence of rent-seeking, innovation and patent race games. Games and Economic Behavior, 44, 217-226.

Baye, M., Kovenock, D., & de-Vries, C.G. (1996). The all-pay auction with complete information. Economic Theory, 8, 291-305.

Baye, M., Kovenock, D., & de-Vries, C.G. (1999). The incidence of overdissipation in rent-seeking contests. Public Choice, 99, 439-454.

Bayus, B., & Mehta, R. (1995). A segmentation model for the targeted marketing of consumer durables. Journal of Marketing Research, 32, 463-469.

Borel, E. (1921). La theorie du jeu les equations integrales a noyau symetrique. Comptes Rendus del Academie. 173, 1304–1308; English translation by Savage, L. (1953). The theory of play and integral equations with skew symmetric kernels. Econometrica, 21, 97-100.

Budd, C., Harris, C., & Vickers, J. (1993). A model of the evolution of duopoly: does the asymmetry between firms tend to increase or decrease? Review of Economic Studies, 60, 543-573.

Cason, T.N., Sheremeta, R.M., & Zhang, J. (2012). Communication and efficiency in competitive coordination games. Games and Economic Behavior, 76, 26-43.

Cason, T.N., Sheremeta, R.M., & Zhang, J. (2016). Asymmetric and endogenous within-group communication in competitive coordination games. Working Paper.

Chen, C., Ong, D., & Sheremeta, R.M. (2015). The gender difference in the value of winning. Economics Letters, 137, 226-229.

Chowdhury, S.M., Kovenock, D., & Sheremeta, R.M. (2013). An experimental investigation of Colonel Blotto games. Economic Theory, 52, 833-861.

Chowdhury, S.M., Sheremeta, R.M., Turocy, T.L. (2014). Overbidding and overspreading in rent-seeking experiments: Cost structure and prize allocation rules. Games and Economic Behavior, 87, 224-238.

Dasgupta, P. (1986). The theory of technological competition. In: Stiglitz, J.E., Mathewson, G.F. (Eds.), New Developments in the Analysis of Market Structure. MIT Press, Cambridge, pp. 519–547.

Davis, D., & Reilly, R. (1998). Do too many cooks spoil the stew? An experimental Analysis of rent-seeking and the role of a strategic buyer. Public Choice, 95, 89-115.

Dechenaux, E., Kovenock, D., & Sheremeta, R.M. (2015). A Survey of experimental research on contests, All-pay auctions and tournaments. Experimental Economics, 18, 609-669.

Deck, C., & Sheremeta, R.M. (2012). Fight or flight? Defending against sequential attacks in the game of siege. Journal of Conflict Resolution, 56, 1069-1088.

Deck, C., Sarangi, S., & Wiser, M. (2016). An experimental investigation of simultaneous multi-battle contests with strategic complementarities. Journal of Economic Psychology, forthcoming.

Deck, C., & Sheremeta, R.M. (2016). Tug-of-war in the laboratory. Working Paper.

Duffy, J., & Matros, A. (2015). Stochastic asymmetric Blotto games: Some new results. Economics Letters, 134, 4-8.

Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10, 171-178.

Fudenberg, D., Gilbert, R., Stiglitz, J., & Tirole, J. (1983). Preemption, leapfrogging and competition in patent races. European Economic Review, 22, 3-31.

Gelder, A. (2014). From custer to thermopylae: Last stand behavior in multi-stage contests. Games and Economic Behavior, 87, 442-466.

Gelder, A., & Kovenock, D. (2015). Dynamic behavior and player types in majoritarian multi-battle contests. ESI Working Paper.

Gelder, A., Kovenock, D., & Sheremeta, R.M. (2016). Behavior in all-pay auctions with ties. Working Paper.

Gneezy, U., & Smorodinsky, R. (2006). All-pay auctions – an experimental study. Journal of Economic Behavior and Organization, 61, 255-275.

Harris, C., & Vickers, J. (1985). Perfect equilibrium in a model of a race. Review of Economic Studies, 52, 193-209.

Harris, C., & Vickers, J. (1987). Racing with uncertainty. Review of Economic Studies, 54, 1-21.

Hart, S. (2008). Discrete Colonel Blotto and general Lotto games. International Journal of Game Theory, 36, 441-460.

Hausken, K. (2008). Whether to attack a terrorist’s resource stock today or tomorrow. Games and Economic Behavior, 64, 548-564.

Hillman, A., & Riley, J.G. (1989). Politically contestable rents and transfers. Economics and Politics, 1, 17-40.

Holt, C., Kydd, A., Razzolini, L., & Sheremeta, R.M. (2016). The paradox of misaligned profiling: Theory and experimental evidence. Journal of Conflict Resolution, 60, 482-500.

Holt, C.A., & Laury, S.K. (2002). Risk aversion and incentive effects. American Economic Review, 92, 1644-1655.

Hortala-Vallve, R. & Llorente-Saguer, A. (2010). A simple mechanism for resolving conflict. Games and Economic Behavior, 70, 375-391.

Irfanoglu, Z.B., Mago, S.D., & Sheremeta, R.M. (2015). The New Hampshire effect: Behavior in sequential and simultaneous election contests. Working Paper.

Klumpp, T., & Polborn, M.K. (2006). Primaries and the New Hampshire effect. Journal of Public Economics, 90, 1073-1114.

Konrad, K.A., & Kovenock, D. (2009). Multi-battle contests. Games and Economic Behavior, 66, 256-274.

Kovenock, D., & Roberson, B. (2012). Conflicts with multiple battlefields. In Michelle R. Garfinkel and Stergios Skaperdas, (Eds.), Oxford Handbook of the Economics of Peace and Conflict.

Kovenock, D., & Roberson, B. (2015). The optimal defense of network connectivity. Working Paper.

Kovenock, D., Roberson, B., & Sheremeta, R.M. (2016). The attack and defense of weakest-link networks. Working Paper.

Kvasov, D. (2007). Contests with limited resources. Journal of Economic Theory, 136, 738-748.

Laslier, J.F. (2002). How two-party competition treats minorities. Review of Economic Design, 7, 297-307.

Lee, T. and Wilde, L. (1980). Market structure and innovation: A reformulation. Quarterly Journal of Economics, 94, 429-436.

Leininger, W. (1991). Patent competition, rent dissipation, and the persistence of monopoly: the role of research budgets. Journal of Economic Theory, 53, 146-172.

Levitin, G., & Hausken, K. (2010). Resource distribution in multiple attacks against a single target. Risk Analysis, 30, 1231-1239.

Llorente-Saguer, A., Sheremeta, R.M., & Szech, N. (2016). Designing contests between heterogeneous contestants: An experimental study of tie-breaks and bid-caps in all-pay auctions. Working Paper.

Loury, G. (1979). Market structure and innovation. Quarterly Journal of Economics, 93, 395-410.

Lugovskyy, V., Puzzello, D., & Tucker, S. (2010). An experimental investigation of overdissipation in the all pay auction. European Economic Review, 54, 974-997.

Mago, S.D., Samek, A., & Sheremeta, R.M. (2016). Facing your opponents: Social Identification and Information Feedback in Contests. Journal of Conflict Resolution, 60, 459-481.

Mago, S.D., Sheremeta, R.M., & Yates, A. (2013). Best-of-three contest experiments: Strategic versus psychological momentum. International Journal of Industrial Organization, 31, 287-296.

McKelvey, R., & Palfrey, T. (1995), Quantal response equilibria for normal form games. Games and Economic Behavior, 10, 6-38.

Milgrom, P. (2007). Package auctions and exchanges. Econometrica, 75, 935-965.

Montero, M., Possajennikov, A., Sefton, M., & Turocy, T.L. (2016). Majoritarian Blotto contests with asymmetric battlefields: An experiment on Apex games. Economic Theory, 61, 55-89.

Myerson, R.B. (1993). Effectiveness of electoral systems for reducing government corruption: A game-theoretic analysis. Games and Economic Behavior, 5, 118-132.

Parco J., Rapoport A., & Amaldoss W. (2005). Two-stage contests with budget constraints: An experimental study. Journal of Mathematical Psychology, 49, 320-338.

Potters, J., de Vries, C.G., & Van Winder, F. (1998). An experimental examination of rational rent-seeking. European Journal of Political Economy, 14, 783-800.

Price, C.R., & Sheremeta, R.M. (2011). Endowment effects in contests. Economics Letters, 111, 217–219.

Price, C.R., & Sheremeta, R.M. (2015). Endowment origin, demographic effects and individual preferences in contests. Journal of Economics and Management Strategy, 24, 597-619.

Roberson, B. (2006). The Colonel Blotto game. Economic Theory, 29, 1-24.

Roberson, B. (2008). Pork-barrel politics, targetable policies, and fiscal federalism. Journal of the European Economic Association, 6, 819-844.

Roberson, B., & Kvasov, D. (2012). The non-constant-sum Colonel Blotto game. Economic Theory, 51, 397-433.

Scotchmer, S. (2006). Innovation and incentives. MIT Press.

Sheremeta, R.M. (2010a). Expenditures and information disclosure in two-stage political contests. Journal of Conflict Resolution, 54, 771-798.

Sheremeta, R.M. (2010b). Experimental comparison of multi-stage and one-stage contests. Games and Economic Behavior, 68, 731-747.

Sheremeta, R.M. (2011). Contest design: An experimental investigation. Economic Inquiry, 49, 573-590.

Sheremeta, R.M. (2013). Overbidding and heterogeneous behavior in contest experiments. Journal of Economic Surveys, 27, 491-514.

Sheremeta, R.M. (2015). Behavioral dimensions of contests. In Congleton, R.D., Hillman, A.L., (Eds.), Companion to the Political Economy of Rent Seeking, London: Edward Elgar, pp. 150-164.

Sheremeta, R.M. (2016). Impulsive behavior in competition: Testing theories of overbidding in rent-seeking contests. Working Paper.

Shupp, R., Sheremeta, R.M., Schmidt, D., & Walker, J. (2013). Resource allocation contests: Experimental evidence. Journal of Economic Psychology, 39, 257-267.

Snyder, J.M. (1989). Election goals and the allocation of campaign resources. Econometrica, 57, 637-660.

Szentes, B., & Rosenthal, R.W. (2003). Beyond chopsticks: Symmetric equilibria in majority auction games. Games and Economic Behavior, 45, 278-295.

Szymanski, S. (2003). The economic design of sporting contests. Journal of Economic Literature, 41, 1137-1187.

Tullock, G. (1980). Efficient rent seeking. In James M. Buchanan, Robert D. Tollison, Gordon Tullock, (Eds.), Toward a theory of the rent-seeking society. College Station, TX: Texas A&M University Press, 97-112.

Zizzo, D.J. (2002). Racing with uncertainty: A patent race experiment. International Journal of Industrial Organization, 20, 877-902.